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Simplifying 0 = 4x2 + 3x + 9 Reorder the terms: 0 = 9 + 3x + 4x2 Solving 0 = 9 + 3x + 4x2 Solving for variable 'x'. Combine like terms: 0 + -9 = -9 -9 + -3x + -4x2 = 9 + 3x + 4x2 + -9 + -3x + -4x2 Reorder the terms: -9 + -3x + -4x2 = 9 + -9 + 3x + -3x + 4x2 + -4x2 Combine like terms: 9 + -9 = 0 -9 + -3x + -4x2 = 0 + 3x + -3x + 4x2 + -4x2 -9 + -3x + -4x2 = 3x + -3x + 4x2 + -4x2 Combine like terms: 3x + -3x = 0 -9 + -3x + -4x2 = 0 + 4x2 + -4x2 -9 + -3x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 -9 + -3x + -4x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(9 + 3x + 4x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(9 + 3x + 4x2)' equal to zero and attempt to solve: Simplifying 9 + 3x + 4x2 = 0 Solving 9 + 3x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 2.25 + 0.75x + x2 = 0 Move the constant term to the right: Add '-2.25' to each side of the equation. 2.25 + 0.75x + -2.25 + x2 = 0 + -2.25 Reorder the terms: 2.25 + -2.25 + 0.75x + x2 = 0 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + 0.75x + x2 = 0 + -2.25 0.75x + x2 = 0 + -2.25 Combine like terms: 0 + -2.25 = -2.25 0.75x + x2 = -2.25 The x term is 0.75x. Take half its coefficient (0.375). Square it (0.140625) and add it to both sides. Add '0.140625' to each side of the equation. 0.75x + 0.140625 + x2 = -2.25 + 0.140625 Reorder the terms: 0.140625 + 0.75x + x2 = -2.25 + 0.140625 Combine like terms: -2.25 + 0.140625 = -2.109375 0.140625 + 0.75x + x2 = -2.109375 Factor a perfect square on the left side: (x + 0.375)(x + 0.375) = -2.109375 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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